Simion Filip
University of Chicago, Chicago, USA

Quadratic forms of signature $(1,n)$ appear naturally in some of the cohomology groups of complex algebraic manifolds. They also appear frequently in cohomology groups that do not, a priori, admit such quadratic forms, and seem to be closely related to the group of (pseudo-)automorphisms of the algebraic manifold.

I will discuss joint work with John Lesieutre and Valentino Tosatti in which we consider some situations of the latter kind where the geometry and dynamics of Calabi-Yau manifolds is controlled by certain hyperbolic reflection groups. The necessary background will be explained.